2010 Prelim

2010 Prelim - 2010 Qualifying Examination 1) Analysis of...

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2010 Qualifying Examination 1) Analysis of Cluster Data A researcher wishes to infer the impact of state labor market characteristics on individual wages with the model w is = + c 0 is ± + g s ² + u is ; where, for individual i in state s : w is - log of weekly earnings c is - m 1 vector of individual characteristics (e.g. education, experience, marital status) g s - employment growth in state s . Thus ² is the coe¢ cient of interest. The sample consists of S states, with state sample sizes ( n 1 ; : : : ; n S ) and overall sample size n = P S s =1 n s . Let X be the n k matrix of regressors. a) Why does the presence of a state-level regressor ( g s ) indicate the errors may be clustered? What is the typical impact on both the estimated coe¢ cients and the estimated standard errors when clustering is accounted for? The researcher A1: u is = ³ s + " is ; (1) where ³ s is independent of " is . Further, let ³ s j X ± i:i:d: (0 ; ´ ) and " is j X ± i:i:d: (0 ; ! 2
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2010 Prelim - 2010 Qualifying Examination 1) Analysis of...

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